Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation

Authors

  • I. P. Mel'nichenko

Abstract

In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is similar to the notion of monogeneity in the complex plane.

Published

25.09.2003

Issue

Section

Short communications

How to Cite

Mel'nichenko, I. P. “Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation”. Ukrains’kyi Matematychnyi Zhurnal, vol. 55, no. 9, Sept. 2003, pp. 1284-90, https://umj.imath.kiev.ua/index.php/umj/article/view/4002.